The primary purpose of this study is to evaluate the safety and tolerability of the combination therapy of trametinib and docetaxel with growth factor support in Japanese subjects with Stage IV or a postoperative recurrence non-small cell lung cancer (NSCLC). This study data will be used for making decision for further Japanese development plan for NSCLC. Six evaluable subjects will be enrolled in a dose level to evaluate the safety and tolerability of the combination treatment. Dose-limiting toxicity will be assessed during the first 21 days of combination therapy.